DELMEDIGO, Joseph Solomon.


אלים. [Sefer Elim].

Amsterdam, Menashe ben Yisrael, 388-389 [1628-29].


FIRST EDITION. Small 4to. 3 parts in 1, separate t-ps to two, pp. (vi) 83 (i) + engraved portrait, without [p]2 (Latin preface) as other copies, probably cancelled; (iv) 190; (ii) 80. Hebrew letter. Portrait of the author trimmed and mounted, repair to verso, typographical border to t-ps, astronomical and scientific diagrams, decorated ornaments. Part 3 bound after Part 1, intermittent light marginal water stain, mostly marginal ink or finger soiling, some marginal repairs, general fairly light browning, gatherings 9-102 and 11-122 of Part I transposed. A well-used but perfectly acceptable copy in modern crushed morocco, two morocco labels, later Hebrew inscription to ffep.

First edition of this extensively illustrated, most important Hebrew work on astronomy, mathematics, natural philosophy, music and geometry, written by ‘the first Jewish Copernican’, student of Galileo and a major influence on Spinoza.

Joseph Solomon Delmedigo (1591-1655) was a rabbi, physician and polymath from Crete. At Padua, he studied medicine and attended Galileo’s astronomy lectures 1609-10. After a brief stay in Venice, he journeyed the Middle East, eventually settling in Amsterdam in 1623, where he wrote ‘Sefer Elim’, his only known work. It is divided into two separately titled parts—‘Sefer Elim’ and ‘Ma’ayan Ganim’—the latter subdivided into four essays on astronomy, mathematics, the consonance of music and biblical passages in relation to the scientific method. ‘Sefer Elim’ is a reply to 12 broad and 70 specific questions posed in letters, reproduced at the beginning, by the Karite scholar Zerah. Delmedigo’s answer discusses Aristotelian natural philosophy, spherical trigonometry, celestial bodies, comets and the workings of the lever, illustrated with diagrams and illustrations.

Whilst Delmedigo’s in-depth analysis of Copernican theories was left unpublished and is now lost, his circumscribed references in ‘Sefer Elim’ are nevertheless revealing. ‘Part of Delmedigo’s support for the Copernican model is to be found in his criticism of the Aristotelian conception of the universe […] By rejecting this idea, Delmedigo not only took on the accepted scientific views of the past, but also challenged the Jewish model of the universe, which was based on Aristotle’; he also stated that the universe was possibly infinite and included other solar systems (Brown, ‘New Heavens’, 70). He mentions studying with ‘his teacher Galileo’, as he describes their observation of the sky and planets through the famous telescope; however, scholars believe Delmedigo became familiar with Copernicanism elsewhere, as until 1610 Galileo was not publicly or privately endorsing this theory (Brown, ‘New Heavens’, 74).

The epistemological inconsistencies of ‘Sefer Elim’ derive from Delmedigo’s complex relationship to the Scientific Revolution and Cabala-informed Jewish culture, resistant to the new method. As proved by the very title—a reference to the fountains of wisdom—he linked ‘Jewish-hermetic revelation with Copernican cosmology and sought material objects such as ancient Hebrew mss that, purportedly, maintained a stronger connection to the revelation’, seeking to connect Jewish theology and Copernicanism (Ben-Zaken, ‘Cross-Cultural’, 78). The work ‘became suspect in the eyes of the elders of the Sephardic community, and a committee was formed to investigate the matter. The book had to be translated orally into Portuguese’; the printer had to declare officially that certain portions would not be published, though by then Delmedigo had moved elsewhere (Heller, ‘C17 Hebrew Book’, 471).

Like the copies at Hebrew Union College and Thomas Fisher Library, this collates with 3 of 4 leaves of preliminaries, lacking the Latin preface on the second. This summarises the content for a non-Hebrew readership, and explains the title. A puzzling addition to a work written entirely in Hebrew, it was probably cancelled for Hebrew-speaking readers. 

Heller, C17 Hebrew book, 470-71; Bib. Hebr. Book, 10125944; Steinschneider, Cat. librorum hebraeorum, 1510-1511, 5960/1-3; Wolf, Bibliotheca Hebraea, I, p.566, n.976. J. Brown, New Heavens and a New Earth (Oxford, 2013); A. Ben Zaken, Cross-Cultural Scientific Exchanges in the Eastern Mediterranean, 1560-1660 (Baltimore, 2010). Not in Riccardi, Houzeau & Lancaster or Lalande.


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EUCLID. Elementorum libri XV.

Pesaro, Camillo Franceschini, 1572. [with]

ARCHIMEDES. Opera non nulla. [and] Commentari.

Venice, Paolo Manuzio, 1558.


FIRST EDITIONS. Folio. Three works in one, ff. (xii) 255 (iv) 55 (ii) 63 (i), first lacking last blank, separate t-p to each. Roman and Italic letter, pages double-ruled in red. First t-p within architectural border t-p, allegorical figures, grotesques, cornucopiae and small geometrical diagrams; second and third with printer’s device to last; hundreds of fine geometrical diagrams; decorated initials. Occasional light yellowing, first t-p with odd marginal thumb mark, light marginal water stains to second t-p and a few ll. where annotations were washed, a few marginal tears without loss, old repairs to 3 ll. and one outer margin of final ll. of first work. Very good, well-margined copies in superb C17 French brown goatskin, gilt to a single- and double-ruled panel design, centre panel with gilt arms of Louis Bizeau surmounted by a plumed helmet, gilt monogram LB to corners, gilt roll of lozenges and circles to edges, all edges gilt and marbled. Spine triple gilt ruled in seven compartments, six with monogram LB, one with gilt lettering, floral scrolls with dentelles at head and foot, raised bands gilt to a roll of interlacing circles. Early casemark ‘FF. 8. 31.’ and armorial bookplate of Viscount Bruce of Ampthill and Baron Bruce of Whorleton, ‘Robert Bruce
1729’ to ffep, a few washed-out early marginalia. In modern slip box.

The superb binding bears the monogram and arms (a fess, two stars in chief, a crescent in point) of Louis Bizeau (fl. first half of C17), a prominent bibliophile of whom little is known (Olivier, ‘Manuel de l’amateur de reliures’, V, pl. 486). Some of his bindings c.1645-50 have been linked to the same workshop as worked for Dominique Séguier (Quaritch, ‘Examples of the Art of Book-Binding’, 108-9). His books, like this, had ruled pages, gilt edges and marbled pastedowns.

Excellent, well-margined copies, in fine impression, of Francesco Commandino’s Latin translations of Euclid’s ‘Elements’ and Archimedes’s ‘opera omnia’, with Commandino’s commentary, the last two issued together. These texts provided the foundations of modern mathematics and physics. Commandino (1509-75) was a humanist from Urbino renowned for his translations of the ancient Greek mathematicians including Aristarchus of Samos and Pappus of Alexandria. Several of his Latin renditions of Greek mathematical terms, for which he relied on previous adaptations by Roman authors like Cicero and Vitruvius, became the standard. Euclid (4 th century BC) was the first to reunite mathematical findings from the ancient world into a coherent, bi-dimensional system centred on simple axioms of plane geometry, based on angles and distance, from which further propositions (or theorems) could be deduced. His ‘Elements’ began with the crucial definition of ‘point’, ‘that which has no part nor size’ and which is only determined by two numbers defining its position in space—the fundamental notion on which the Euclidean geometrical system is based. Archimedes (287-12BC) was a mathematician, inventor, astronomer and engineer from Syracuse. The ‘Opera non nulla’ includes all his recorded writings, except for the treatise on floating bodies and that on the method of mechanical theorems, which was discovered later. This edition—the sole Aldine of Archimedes’s works—illustrates superbly his theorems on the area of circles, parabolae, spirals, spheres and cones, concluding with the famous ‘De arenae numero’, a calculation of the amount of sand grains needed to fill the universe. It is followed by Commandino’s commentary on Archimedes’s works, where geometrical diagrams are substituted by numerical calculations.

Charles Bruce (1682-1747), Earl of Ailesbury, Viscount Bruce of Ampthill and Baron Bruce of Whorleton, was a keen book collector. A catalogue of his vast library, comprising over 8,000 volumes, at Tottenham in Wiltshire, was printed in 1733—the second earliest catalogue of an English private library ever published (Pollard & Ehrman, 274-75), this copy being n.17, p.83. The library was eventually sold at Sotheby’s in 1919. His first-born, who died in 1738 before succeeding his father, is probably the Robert Bruce who signed the copy in 1729.

I) USTC 828478; BM STC It., p. 238; Brunet II, 1088: ‘édition bonne de cette traduction estimée’ ; Riccardi I, 362; Mortimer, Harvard Italian, 174; Thomas-Stanford, 18.

II) USTC 810251; BM STC It., p. 36; Rénouard 173:3; Riccardi I, 42: ‘bella edizione, assai poco comune’; Brunet I, 344: ‘peu commune’.


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TUNSTALL, Cuthbert


De arte supputandi libri quartuor.

London, In aedibus Richardi Pynsoni, Anno Verbi incarnati. 14 Oct. 1522


FIRST EDITION. 4to. 204 unnumbered leaves. A-S⁴, T⁶, TV⁶, V⁶, X-Z⁴, a⁴, ab⁶, b-z⁴, &⁴. Roman letter. Title within a fine historiated woodcut border signed HH and copied from Holbein (McKerrow & Ferguson 8), errata on verso, floriated white on black criblé woodcut initials, woodcut mathematical tables, errata crossed out in an early hand with the corresponding corrections added throughout, occasional manuscript underlining. British Museum sale duplicate 1787, stamp on title, manuscript date “June 18th 1813″, on rear flyleaf in Michael Wodhull’s hand (1740-1816), bookplate and label of George Dunn (1865-1912), Woolley Hall, on pastedown, mss. note in pencil in his hand “Wodhull’s copy, see fly leaf at end.” with his distinctive price code and date March 1910, “John Burns, May 23 1918”, mss above, Erwin Tomash label above. Light age yellowing, a few quires lightly browned, some minor marginal spotting, title a little dusty with thumb marks at margin, the occasional mark or ink splash. A very good copy, generally crisp and clean, with good margins, some deckle edges, in late C18th calf, covers bordered with a single gilt rule, spine, rebacked with former spine laid down, gilt ruled in compartments, red morocco labels gilt lettered, a.e.g. corners a little worn, a little rubbed. 

First edition of the first English book wholly on arithmetic, by the great Catholic humanist, Cuthbert Tunstall (1474-1559). The work was Tunstall’s farewell to secular scholarship as he was made Bishop of London a few days after its publication, and thereafter Lord Privy Seal. He wrote it so that his friends could make their own calculations and no longer be cheated by money changers. It is designed as a practical work on arithmetic with the emphasis on commercial transactions, undoubtedly based on models Tunstall encountered during his studies in Padua. “The book includes many business applications of the day, such as partnership, profit and loss and exchange. It also includes the rule of false, the rule of three and numerous applications of these and other rules. It is, however, the work of a scholar and a classicist rather than a businessman.” Smith p.134, It is dedicated to his particular friend Thomas More, who, the previous year had been appointed sub-Treasurer of England, because there was no more appropriate dedicatee than the man engaged in supervising the finances of the King This was also the return of the compliment which, six years earlier, More had paid Tunstall in the opening lines of the Utopia. The work was actually rather too scholarly for ordinary businessmen and it was not reprinted in England. However, it achieved some success on the continent and Rabelais (Oeuvres II 222) mentions it as required reading for the young Gargantua in Paris; it was also prescribed as an arithmetical study text in the Oxford statues of 1549, (together with Cardano).“The dedicatory epistle to M[ore], gives an interesting picture of M[ore] and Tunstall” Gibson 157.

“Cuthbert Tunstall began his studies in Oxford but soon moved to Cambridge because of the plague. He later studied Canon and Roman law at Padua. He held several appointments in Henry VIII’s court and was made Bishop of London only a few days after this work was published. This is the first complete work on arithmetic to be published in England. It was preceded only by a chapter in Caxton’s Myrrour of the World, published in 1481. .. In content and structure the work resembles that by Luca Pacioli and other Continental arithmetics, which Tunstall undoubtedly encountered in Padua or during his extensive travels for Henry VIII. An unusual feature in the book is the separate tables for addition and subtraction as well as those usually found for multiplication. .. Robert Recorde’s English language arithmetic appeared fifteen years later in 1537 and seems to have eclipsed Tunstall’s work, at least in England. The title page is a revised version of one by Hans Holbein, whose initials can be seen on the left border. The woodcut was first used by a printer in Basel in 1516.” Erwin Tomash.

Michael Wodhull studied at Winchester school when Joseph Warton was second master; he later attended Brasenose College Oxford. He was high sheriff of Northamptonshire in 1783. Wodhull wrote poetry, collected first editions of classics and incunabula, and contributed many items to the Gentleman’s Magazine under the signature “L. L.” One of his Euripides translations appeared in an Everyman’s Library edition. The character “Orlando” in Thomas Frognall Dibdin’s Bibliomania is supposed to represent Wodhull. Dunn was a bibliophile who amassed a splendid library with particular strengths in early printing, law books and medieval manuscripts. His remarkable collection was sold in a number of sales between 1913 and 1917. 

ESTC S118552. STC 24319. Tomash & Williams T57 (this copy) Smith, Rara arithmetica, pp.132-4


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Λογαριθμοτεχυια or the construction and use of the logar-ithmeticall tables by the helpe whereof, multiplication is performed by addition, division by subtraction, the extraction of the square root by bipartition, and the cube root by tripartition, &c..

London, Miles Flesher, 1648


Une table logarithmetique par laquelle on peut trouver le logarithme de quelque numbre que ce soit dessous 400000.

London [Printed by M. Flesher], 1635


24mo. Two works in one. pp. [viii], 135, [i], [clvi]. A–F12, a–F12, G6, ()1. Roman and Italic letter, text within box rule. Floriated woodcut initials, typographical ornaments, mathematical woodcuts in text, ‘Strathnaver’ in near contemporary hand on ff-ep and at head of t-p., Erwin Tomash’s label on front pastedown. Light age yellowing. A very good copy, crisp and clean in contemporary speckled calf, covers bordered with a double blind rule, spine double ruled in compartments, red morocco label gilt, e.e.r.

A very good copy of the third edition of this rare work on logarithms. In 1624, when Wingate was in France, he produced a short tract on logarithms in which he indicates: ‘I…had the happinesse to be the first transporter of the use of these inventions into those parts.’ In 1626, he translated his French work into English and it became the first edition of this book. In the preface he indicates that it is nothing more than a condensation of the work of Henry Briggs’ Arithmetic logarithmica, which he must have acquired shortly before he left London as it was only published in 1624. This is the third edition (all of them edited by Wingate). It consists of a series of twenty-eight problems covering everything from simple multiplication to spherical geometry, followed by an appendix containing another forty-six problems in which he briefly discusses, usually in one sentence, the rule for finding the answer. The tables were apparently printed separately, perhaps for a French edition in 1635. They have French titles on both the tables and the column headings. The paper also has a different watermark from that used to print the text. Wingate’s work on arithmetic ‘Of natural and artificial arithmetick’ was used in many English schools and remained in print for more than a century. It established Wingate’s name as a writer of texts and did more for his reputation than any of his more advanced works on logarithms or instruments.

Wingate was born in Yorkshire and studied law at Oxford. Although he remained a lawyer, he was an avid amateur mathematician and writer of mathematical texts. He spent twenty-six years in Paris, where, among other things, he was tutor to the French princess Henrietta Maria. It was during his early days in Paris that he published two works (Construction, description et usage de la règle de proportion, 1624, and Arithmétique logarithmique, 1626) that introduced logarithms to the French. He returned to England in 1650 and entered politics but continued to write on mathematical subjects.

“After groundbreaking publications by the British mathematicians John Napier and Henry Briggs, Edmund Wingate, an English mathematician who was temporally based in Paris, emphasised the power of the combination of decimal fractions and common logarithms – that is to say, logarithms to the base of 10 – to assist practitioners, such as surveyors navigators and carpenters , to make the kind of calculations that they were likely to need to make in their daily workplace. On returning to England, Wingate wrote a text designed for use in schools, in which he advocated the application of decimal fractions and logarithms as a way of simplifying calculations.  M.A. Clements ‘Thomas Jefferson and his Decimals 1775–1810.’

1) ESTC R219767. Wing W3018A. Tomash & Williams W97 (This copy). 2) ESTC S95890. STC 25851.5. Tomash & Williams W98. (this copy)


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Kitāb Al Fawayīd wa al-Ṣilāt Wa al-‘Awāyid [On Magic and Talismans]

[Sana’a, Yemen, AH 969/1562]


Arabic manuscript on paper, 100 ff. of text, two free end papers, pages numbered, each with 25 lines of black naskh script, text panel 157 x 100 mm, titles and some words picked out in red, some phrases underlined in red, text within red frame, including numerous arithmetical tables and some diagrams, later notes to the end papers, colophon signed ‘Abd al-Raḥīm al-Zubaydi in Sana’a in modern Yemen in Shawwal AH 969 (June-July 1562 AD) and dated, repair without loss, at least three different hands of marginal annotations.

Contemporary, polished natural high quality morocco with central stamped medallion, an excellent copy with minor damp staining and marginal finger-soiling.

Kitāb Al Fawayīd wa al-ilāt Wa al-‘Awāyid is a treatise outlining the various principles of numerology in Islam where charts and numbers are used for divination or to bring barākā (blessings). Most of the illustrations in this manuscript are of the Islamic talismanic design known as wafq – ‘magic squares’ (see Maddison, F., and Savage-Smith E., ‘Science, Tools & Magic in the Khalili Collection of Islamic Art’, Oxford; Oxford University Press, 1997 or Savage-Smith, E., ‘Magic and divination in early Islam’, Aldershot; Ashgate Variorum, 2004). A magic square is arranged to produce a constant sum in all rows and columns and were most commonly depicted on amulets or manuscripts. The wafq is sometimes described as ‘recreational mathematics’ because of the sophisticated mathematical principles they illustrate. Jacques Sesiano in the article ‘Magic squares in Islamic Mathematics’ has argued that magic squares in Medieval Islam were developed from chess which was hugely popular in the Middle East. Sesiano has also observed how there are references to the use of magic squares in astrological calculations. Magic squares are, generally, magic by association (because of the carefully arranged sums), physical proximity and in their supposed capacity to foretell future outcomes.Rare.

From the collection of Adrienne Minassian; formerly at Brown University.


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De gli elementi d’Euclide.

Urbino, D. Frisolino, 1575.


FIRST EDITION thus. ff. (viii) 278. Roman letter, with Italic. All pages with typographical border, c.600 woodcut illustrations. One lower outer corner torn not touching text, a few tiny holes to lower margin of t-p. A very good copy, on blue paper, in early C17 calf, double gilt ruled, raised bands, spine in seven compartments, repaired at head and foot, one gilt-lettered, others double gilt ruled with large gilt fleuron. Modern bibliographical notes pencilled to front pastedowns and fep, earlier inked to rear pastedown and fly, C19 engraved bookplate c1800 of Conte della Trinità to front pastedown, erased early ex-libris to t-p, occasional Italian annotation.

This outstanding copy was printed on blue paper for presentation. No copies on blue paper of this edition are recorded in major bibliographies or at US libraries. Intended as a substitute for parchment, blue paper was first employed by Aldus, and perfected by Giolito, for ‘deluxe’ copies prepared for important personalities. It became an increasingly widespread practice with selected copies of particularly scientific and architectural works in the course of the C16. The translator and commentator of this edition, Federico Commandino, had also overseen the printing on blue paper of a limited Latin edition of Euclid’s ‘Elements’ in 1572.

Very rare copy, on blue paper, of the first Italian translation of Euclid’s ‘Elements’ edited by Federico Commandino. Commandino (1509-75) was a humanist from Urbino renowned for his translations of the works of ancient Greek mathematicians including Aristarchus of Samos and Pappus of Alexandria. Several of his Latin (and later vernacular) renditions of Greek mathematical terms, for which he relied on previous adaptations by Roman authors like Cicero and Vitruvius, became the standard. Euclid (4th century BC) was the first to reunite mathematical theories from the ancient world into a coherent, bi-dimensional system centred on simple axioms of plane geometry, based on angles and distance, from which further propositions (or theorems) could be deduced. His ‘Elements’ began with the crucial definition of ‘point’, ‘that which has no part nor size’ and which is only determined by two numbers defining its position in space—the fundamental notion on which the Euclidean geometrical system is based. The fifteen books of the work, the last two of which are now considered spurious, discuss plane and solid geometry, the theory of proportion and the properties of rational and irrational numbers. Euclid’s ‘Elements’ was commonly used in schools for centuries and is ‘the oldest mathematical textbook in the world’ (PMM 25).

This copy belonged to an early mathematician who wrote a long marginal re-phrasing of a corollary. Between the late C18 and early C19, it was in the collection of the bibliophile Count Remigio Filiberto Costa della Trinità.

USTC 828481; Riccardi I/1, 363; Thomas-Stanford 42; BM STC It., p. 568; Honeyman II, 1009 and 1010. Not in Brunet or Mortimer.


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An institution trigonometricall. the doctrine of the dimension of plane and sphericall triangles.

London, William Iones dwelling in Red-crosse-streete, 1635


FIRST EDITION. pp. [ii], 78, [332]. A–E8, A–R8, S6, T–X8. [without S7-8 blank]. Roman and Italic letter. Small typographical ornament on title, floriated woodcut initials, typographical headpieces, numerous woodcut diagrams in text, 332 pages of tables, book-label of Erwin Tomash on pastedown, “Lewis Dyve” on title in an slightly later hand with price 3/6. Light age yellowing. A very good copy, crisp and clean with many deckle edges, in contemporary calf, covers bordered with a a double blind rule, spine double blind ruled in compartments, later green paper label, brass catches, remains of clasps, stubbs from a printed bible leaf a.e.r. 

First edition of this important and influential work on trigonometry, with most interesting contemporary provenance. Gellibrand had been a student at Trinity College, Oxford, when he was introduced to mathematics and became acquainted with Henry Briggs. After graduation he was ordained and took a job as curate in a small town in Kent. When Edmund Gunter died in 1626, Gellibrand applied for his post as professor of astronomy at Gresham College and was elected in early 1627. One of his sponsors was Henry Briggs, and Gellibrand repaid the debt by completing the second volume of Briggs’ Trigonometria Britannica and seeing it through the press after Briggs died in 1630. “He .. became a friend of Henry Briggs, on whose recommendation he was chosen professor of astronomy at Gresham College, 2 Jan. 1626–7. Briggs dying in 1630 he left his unfinished ‘Trigonometria Britannica’ to Gellibrand. Gellibrand held puritan meetings in his rooms, and encouraged his servant, William Beale, to publish an almanack for 1631, in which the popish saints were superseded by those in Foxe’s ‘Book of Martyrs.’ Laud, then bishop of London, cited them both into the high commission court. They were acquitted on the ground that similar almanacks had been printed before, Laud alone dissenting, and this prosecution formed afterwards one of the articles exhibited against him at his own trial. In 1632 Gellibrand completed Briggs’s manuscript, and published it in 1633 as ‘Trigonometria Britannica’ According to Ward, an English translation of Gellibrand’s book was published in 1658 by John Newton as the second part of a folio with the same title. During 1633 he also contributed ‘An Appendix concerning Longitude’ to ‘The strange and dangerous Voyage of Captaine Thomas James,’ 4to, 1633, which has been frequently reprinted. Gellibrand died of fever 16 Feb. 1636, and was buried in the church of St. Peter the Poor, Broad Street, London.” DNB. Gellibrand is also known for his discovery of magnetic declination and for application of mathematics and astronomy to practical problems of navigation. This book contains two brief expositions on plane and spherical triangles followed by a major section consisting of trigonometric functions, logarithms and navigational and astronomical tables.

Sir Lewis Dyve (1599–1669) was an English Member of Parliament and a Royalist during the English Civil War; he was knighted in 1620 and was one of the attendants of Prince Charles at Madrid. He was elected MP for Bridport in the Parliaments of 1625 and 1626, and for Weymouth in that of 1628. Dyve fought for the Royalist cause and was captured at the siege of  Sherborne, later imprisoned in the Tower of London from 1645 to 1647. Being moved to the King’s Bench, he escaped, but was recaptured at Preston. Imprisoned in  Whitehall he escaped once more, according to his own account on the very day he was to have been executed; John Evelyn records in his Diary on 6 September 1651 that Dyve dined with him and related the story of his “leaping down out of a jakes two stories high into the  Thames at high water, in the coldest of winter, and at night; so as by swimming he got to a boat that attended for him, though he was guarded by six musketeers. Dyve then made his way to  Ireland where he once more served with the Royal forces; in 1650 he published an account of events in that country during the previous two years. He lost much of his fortune through his loyalty to the Crown, but also in part due to heavy gambling: in 1668, the year before he died, Samuel Pepys called him disapprovingly “a great gamester”.

A very good copy of this rare work. ESTC cites two copies recorded in the US only; at the Folger and Huntington.

ESTC S125464. STC 11712.5. Tomash G30. Henderson pp.62-63 no 33.0


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FABRI, Ottavio


L’uso della squadra mobile.

Venice, appresso Francesco Bariletti, 1598.


FIRST EDITION. 4to. pp. (ii) 58 (vi), without the ‘squadra mobile’ plate as usual. Italic letter, with Roman. Engraved architectural t-p with female allegorical figures, putti and globe, 25 half-page engraved illustrations, decorated initials, head- and tailpieces. Little thumbing or minor marginal spotting in a few places, one plate superimposed presumably by way of correction. An excellent wide-margined copy, on thick paper, in old carta rustica, recased, bookplate of Erwin Tomash to front pastedown, the odd contemporary marginalia. In modern folding box.

An excellent copy of the first edition of this important work on the application of triangulation. Ottavio Fabri (fl. late C16-early C17) was an Italian mathematician of whom little is known. His greatest contribution to the discipline, immortalized in this work, was the invention of the ‘squadra mobile’, a brass geometrical instrument to ‘measure, level and transfer onto paper every distance, height and depth’, with applications in astronomy, geometry and the measuring of terrain. The edition was printed in two issues with differing preliminaries, though no priority has been established. The first section is devoted to measurements and includes comparisons between units used in different cities (the ‘Braccio toscano’ in Florence, the ‘Tornadure’ in Cervia) or countries (‘Piedi’ in France and the Trevigian ‘Pertica’ in Cologne). He proceeds to explain the construction of the instrument; this part was illustrated by an engraved plate portraying the ‘squadra mobile’, absent in most copies. The best material for the instrument, he found, is copper, a piece of which—‘as thick as a knife’s back’—can be bought ‘from any ironmonger in town’. He even advertised the best craftsman in Venice to assemble the instrument, ‘M. Battista…degli Horologli’ in his Spadaria shop, who made clocks and scales. The rest, illustrated with handsome engravings, explains the most common applications of the instruments in measuring from various positions the distance, depth and height, in relative and absolute terms, of buildings, hills, allotments, etc. The ‘squadra mobile’ could even be used to map a city’s area without a compass both from inside or outside its walls. Illustration XIII pasted on p. 37 appears to have been an editorial afterthought as it is also found in the NYPL copy.

Riccardi I/1, 433-34; BM STC It., p. 241; Brunet II, 1151 (mentions this ed.); Honeyman IV, 1259 (1615 ed.).  


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PITISCUS, Bartholomaeus


Trigonometriae sive. De dimensione triangulorum libri quinque.

Augsburg, Michael Manger, Dominicus Custos, 1600.


FIRST EDITION. 4to. 2 parts in 1, continuous pagination, additional typographical t-p to second, pp. (viii) 213 (iii) 215 [217]-370 [372] (ii), variant probably, first issue, without errata. Roman letter, with Italic. Engraved t-p with four figures of mathematicians, woodcut geographical diagrams and tables, woodcut printer’s device to recto of penultimate leaf, decorated tailpieces. Slight marginal dust-soiling to t-p, edges untrimmed and a bit dusty, two sheets of early mathematical diagrams (loosely inserted). An excellent copy in carta rustica, lacking one of four ties, bookplates of Auersperg library and Erwin Tomash to front pastedown, autograph of Wolfgang Engelbrecht von Auersperg and his catalogue entry dated 1656 to lower and upper t-p respectively, occasional contemporary annotation based on printed errata. In modern folding box.

An excellent copy of this ground-breaking mathematical work. Bartholomaeus Pitiscus (1561-1613) was a German theologian, mathematician and astronomer, tutor to the young Frederick IV, Count Palatine, and court chaplain at Breslau. First published in 1595, ‘Trigonometriae’ introduced the neologism ‘trigonometry’ into the Latin and vernacular language of mathematics, with the opening statement: ‘Trigonometria est doctrina de dimensione Triangulorum.’ It was a subject dating back to antiquity which only expanded exponentially in the C16 due to the demands of navigation and cartography. Divided in five parts, the work is a very thorough and clear manual laying down point by point, through very short statements, the basics of the subjects of plane and spherical trigonometry—e.g., the geometrical nature of triangles, the workings of straight lines, the translation of triangles onto spherical surfaces, trigonometric functions, sinus and cosinus, illustrated with schemas and accompanied by mathematical tables. Pitiscus calls the following ‘the golden rule of arithmetic’—‘if we take four numbers which are proportional to one another, given three it is possible to find the fourth.’ The last part is concerned with the practical applications of trigonometry in the calculation of irregular geographical surfaces, of the height of a building given one’s distance from it, latitude and longitude, and the height of the sun in relation to the horizon. Although without the two leaves of errata, the contemporary annotator—a mathematician—appears to have had access to them as he marked a passage as ‘error’ and amended its complex calculation with a six-figure result. Probably the same annotator also left two paper slips with drawings and operations of spherical trigonometry.  

Wolfgang Engelbrecht (1610-73), Count of Auersperg, was an Austrian politician and patron of the arts.

USTC 615235; Adams 1331 (with errata); Brunet IV, 679. Not in Riccardi, Smith or BM STC It. C17.


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GALILEI, Galileo


La operazione del compasso geometrico.

Padua, per Paolo Frambotto, 1640.


4to. pp. (viii) 80, 2 fold-out plates. Roman letter, little Italic. Woodcut printer’s device to t-p, fold-out plate with engraved astronomical diagrams, line and woodcut illustrations, decorated initials and headpieces. Faint ink spots to t-p, slight foxing in places, couple of gatherings browned, two holes at gutter of last touching a letter. A very good copy in carta rustica, later eps. Bookplate of Erwin Tomash to front pastedown, armorial bookplate of Ricasoli Firidolei to verso of t-p. In modern folding box.

Very good copy of the second edition—the first with the plate—of this major work in the history of computing. The world-renowned symbol of Renaissance scientific progress, the Italian astronomer and physician Galileo Galilei (1564-1642) was professor at Pisa and Padua, and the inventor of scientific instruments like the thermoscope (an early thermometer) and, most famously, a more powerful telescope with which he first identified, among other major discoveries, Jupiter’s four moons. His support of heliocentric theories and Copernicanism caused him accusations of heresy against which he was summoned to defend himself in front of the Inquisition. The ‘compasso geometrico’ was another of his creations, first discussed in print in 1606. Made of two rulers joined by a volvelle—as shown in the engraved plates—the compass could be used to calculate distance, height, depth and a variety of proportional operations through a system of scales based on Euclid’s study of triangles. In the dedicatory letter, the printer Frambotto celebrated Galileo’s ‘maraviglioso compasso’ as having ‘fundamental importance for the art of war’ and being ‘sought after by leading Captains’; it also addressed everyday problems in civil life. After explaining how the ruler on the compass is subdivided into sections, he proceeds to explore different applications. These include theoretical operations like cube roots, the squaring of a circle and geometrical proportions, as well as practical ones like the scale increase or reduction of the plan of a geographical area, the translation of prices from one currency to another according to their relative value, the calculation of interests and the arithmetic subdivision of armies on the battlefield. In his letter to the reader, Galileo stated that his ‘compasso’ would allow ‘anyone to solve in an instant the most difficult arithmetical operations’ without being skilled mathematicians.      

Tomash & Williams G12; Brunet II, 1462: ‘très rare’; Honeyman IV, 1395; Riccardi I/1, 506: ‘buona edizione’. Not in BM STC It. C17 or Smith, Rara.


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